Here, as in [1]}, \(G(\lambda _a(\mu ))\)  is the isotropy group at \(\lambda _a(\mu )\)  for the \(G\)  action; \(\mathfrak {h}\)  is the complexified Lie algebra of a maximally split \(\theta \) -stable Cartan subgroup \(H=TA\)  of \(G(\lambda _a(\mu ))\) . Note that \(\nu \)  in (REF ) has the same norm as the \(\nu \) -part in the atlas final parameter \(p=(x, \lambda , \nu )\)  of \(\pi \) . We will not distinguish them by abusing the notation a bit.
